Microphase separation in semicrystalline block copolymers can be driven by two forces : thermodynamic incompatibility between the blocks in the melt or crystallization of one or more blocks. The diblock copolymers investigated here are polyethylene-b-poly(3-methyl-1-butene), all containing approximate to 26 wt % ethylene, prepared by hydrogenating high-1,4-polybutadiene-b-high-3,4-polyisoprene. This block asymmetry leads to a hexagonally-packed cylindrical morphology when microphase separation is present in the melt. The molecular weights are varied to obtain differing degrees of incompatibility in the melt, ranging from a single-phase (disordered) melt to a strongly segregated melt. X-ray scattering and differential scanning calorimetry are used to investigate the morphology resulting from crystallization in these melts as a function of thermal history. Crystallization from strongly segregated melts is confined to the cylindrical microdomains and produces a morphology essentially independent of thermal history. In the most strongly segregated diblock crystallized at 10-20 degrees C/min, chain folding within these cylindrical microdomains is preferentially oriented with the chain axis tilted 18 +/- 4 degrees from normal to the cylinder axis. In contrast to strongly segregated melts, the morphology produced by crystallization from weakly segregated melts is highly dependent upon thermal history. Faster cooling kinetically confines crystallization to cylinders, while slower cooling results in complete disruption of the cylindrical melt mesophase upon crystallization, leading to a lamellar morphology with a larger domain spacing.